Composite structures, such as those that are constructed of fiber reinforced composite materials, typically are formed by conforming pre-cured or partially cured flexible sheets of composite material to a rigid mold. Depending on the ultimate structure being formed, the mold may be required to have very precise tolerances relative to a desired ultimate shape of the structure being formed. Such molds, especially when very large, are very expensive to construct and maintain. Moreover, due to the nature of conforming a generally planar sheet of material to a mold having contours, including complex contours, it often is difficult to avoid imparting undesired wrinkles to the composite material. Such wrinkling or other anomalies created during forming may not be acceptable to meet the performance requirements of the final composite structure.